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v.s Group Title

Find equations of the tangent line and normal line to the curve at the given point. y = x^4 + 4e^x, (0, 4) tangent line y = normal line y =

  • one year ago
  • one year ago

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  1. campbell_st Group Title
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    can you find the derivative of the curve...?

    • one year ago
  2. v.s Group Title
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    i don't know

    • one year ago
  3. campbell_st Group Title
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    ok... have you done or are you doing calculus?

    • one year ago
  4. v.s Group Title
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    doing calculus

    • one year ago
  5. campbell_st Group Title
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    ok... can you differentiate y = x^4...?

    • one year ago
  6. v.s Group Title
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    4x^3

    • one year ago
  7. campbell_st Group Title
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    and can you differentiate \[ y = 4e^{x} \]

    • one year ago
  8. v.s Group Title
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    x4e

    • one year ago
  9. v.s Group Title
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    or is it x4e^-x

    • one year ago
  10. campbell_st Group Title
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    quick lesson \[y = 4e^{f(x)} ..... then .... y'=4f'(x) e^{f(x)}\] and in your question f(x) = x... try the derivative again for \[y = 4e^x\]

    • one year ago
  11. v.s Group Title
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    4xe^-x

    • one year ago
  12. campbell_st Group Title
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    not quite if f(x) = x f'(x) = 1 so its y' = 4e^x so you you function the derivative is \[y' = 4x^3 + 4e^x\] ok... you now have the equation for the slop of the tangent...(1st derivative) subsitiute x = 0 to find the slope of the tangent at the point (0, 4)

    • one year ago
  13. v.s Group Title
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    y'=4

    • one year ago
  14. campbell_st Group Title
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    thats correct so you have a tangent or line with a slope of 4 and point (0, 4) can you find the equation of the line...? for the normal... the slope will be the negative reciprocal of the slope of the tangent... what would the slope of the normal be..?

    • one year ago
  15. v.s Group Title
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    =-1/4x^3+4e^x

    • one year ago
  16. campbell_st Group Title
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    no... ok... lets step back... you have a slope of 4 and point (0, 4) the equation of the tangent will be y = 4x + b or using the formula \[y - 4 = 4(x - 0)\] whats the equation of the tangent...?

    • one year ago
  17. v.s Group Title
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    y=4x-4

    • one year ago
  18. campbell_st Group Title
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    can you try again..

    • one year ago
  19. v.s Group Title
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    y=4x+4

    • one year ago
  20. campbell_st Group Title
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    ok... thats the equation of the tangent... now the normal... which is perpendicular to the tangent... the slope is the negative reciprocal of the tangent... so if the tangent has a slope of 4 ... what is the slope of the normal..?

    • one year ago
  21. v.s Group Title
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    y=-1/4x+4

    • one year ago
  22. campbell_st Group Title
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    that looks good... so there you have your solutions.

    • one year ago
  23. v.s Group Title
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    thank you

    • one year ago
  24. campbell_st Group Title
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    hope it helps... you do need to practice you differentiation basics.

    • one year ago
  25. v.s Group Title
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    yeaa

    • one year ago
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