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v.s

  • 2 years ago

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 =

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  1. campbell_st
    • 2 years ago
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    can you find the derivative of the curve...?

  2. v.s
    • 2 years ago
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    i don't know

  3. campbell_st
    • 2 years ago
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    ok... have you done or are you doing calculus?

  4. v.s
    • 2 years ago
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    doing calculus

  5. campbell_st
    • 2 years ago
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    ok... can you differentiate y = x^4...?

  6. v.s
    • 2 years ago
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    4x^3

  7. campbell_st
    • 2 years ago
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    and can you differentiate \[ y = 4e^{x} \]

  8. v.s
    • 2 years ago
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    x4e

  9. v.s
    • 2 years ago
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    or is it x4e^-x

  10. campbell_st
    • 2 years ago
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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 \[y = 4e^x\]

  11. v.s
    • 2 years ago
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    4xe^-x

  12. campbell_st
    • 2 years ago
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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)

  13. v.s
    • 2 years ago
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    y'=4

  14. campbell_st
    • 2 years ago
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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..?

  15. v.s
    • 2 years ago
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    =-1/4x^3+4e^x

  16. campbell_st
    • 2 years ago
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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...?

  17. v.s
    • 2 years ago
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    y=4x-4

  18. campbell_st
    • 2 years ago
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    can you try again..

  19. v.s
    • 2 years ago
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    y=4x+4

  20. campbell_st
    • 2 years ago
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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..?

  21. v.s
    • 2 years ago
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    y=-1/4x+4

  22. campbell_st
    • 2 years ago
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    that looks good... so there you have your solutions.

  23. v.s
    • 2 years ago
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    thank you

  24. campbell_st
    • 2 years ago
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    hope it helps... you do need to practice you differentiation basics.

  25. v.s
    • 2 years ago
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    yeaa

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