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clara1223

  • one year ago

f(x)=(x^2)+1+(1/(x^4)), c=1; (a) find the slope of the line that is tangent to the graph of f(x) at the given point x=c; (b) write an equation of the tangent line to the graph of f(x) at the point (c,f(c))

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  1. misty1212
    • one year ago
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    HI!!

  2. misty1212
    • one year ago
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    \[f(x)=x^2+1+\frac{1}{x^4}\]?

  3. clara1223
    • one year ago
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    yep!

  4. misty1212
    • one year ago
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    do you know the derivative?

  5. misty1212
    • one year ago
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    lol another county heard from you got \(f'(x)\) if not let me know

  6. clara1223
    • one year ago
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    I get that the derivative is 2x-(4/(x^5))

  7. clara1223
    • one year ago
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    yeah this is calc

  8. misty1212
    • one year ago
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    ok looks good plug in 1 what do you get?

  9. clara1223
    • one year ago
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    -2

  10. misty1212
    • one year ago
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    ok so \(m=-2\) next i guess find \(f(1)\)

  11. misty1212
    • one year ago
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    oh, the answer to question 1 was \(-2\) now we can find the equation of the tangent line, once we have the point

  12. clara1223
    • one year ago
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    how do you construct the equation of the tangent line? I know in class we use y-y1=m(x-x1) and that m=f'(c) but what are y1 and x1?

  13. anonymous
    • one year ago
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    \[x_1=1,y_1=f(1)\]

  14. clara1223
    • one year ago
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    Oh! duh! (c,f(c)). the question told me that. thanks!!

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