Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

{:[f^(')(x)=8x^(3)-12 x" and "f(1)=1],[f(-2)=]:}

f′(x)=8x3−12x and f(1)=1f(−2)= \begin{array}{l}f^{\prime}(x)=8 x^{3}-12 x \text { and } f(1)=1 \\ f(-2)=\end{array}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Calculusright chevron icon
Find derivatives of sine and cosine functionsright chevron icon

Full solution

Q. f′(x)=8x3−12x and f(1)=1f(−2)= \begin{array}{l}f^{\prime}(x)=8 x^{3}-12 x \text { and } f(1)=1 \\ f(-2)=\end{array}
  1. Calculate f(1)f(1): Calculate f(1)f(1) directly from the given information.\newlinef(1)=1f(1) = 1
  2. Integrate f′(x)f'(x): To find f(−2)f(-2), integrate f′(x)f'(x) to get f(x)f(x). The integral of f′(x)=8x3−12xf'(x) = 8x^3 - 12x is:\newline∫(8x3−12x)dx=2x4−6x2+C\int(8x^3 - 12x) dx = 2x^4 - 6x^2 + C, where CC is the constant of integration.
  3. Find Constant CC: Use the given f(1)=1f(1) = 1 to find CC.
    1=2(1)4−6(1)2+C1 = 2(1)^4 - 6(1)^2 + C
    1=2−6+C1 = 2 - 6 + C
    C=5C = 5
  4. Substitute x=−2x = -2: Now substitute x=−2x = -2 into f(x)=2x4−6x2+5f(x) = 2x^4 - 6x^2 + 5 to find f(−2)f(-2).
    f(−2)=2(−2)4−6(−2)2+5f(-2) = 2(-2)^4 - 6(-2)^2 + 5
    f(−2)=2(16)−6(4)+5f(-2) = 2(16) - 6(4) + 5
    f(−2)=32−24+5f(-2) = 32 - 24 + 5
    f(−2)=13f(-2) = 13

More problems from Find derivatives of sine and cosine functions

Question
Find the derivative of f(x) f(x) .\newlinef(x)=cos⁡(x) f(x) = \cos(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡(x) f(x) = \tan(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ex f(x) = e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=ln⁡(x) f(x) = \ln(x) \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=tan⁡−1x f(x) = \tan^{-1}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) .\newlinef(x)=xex f(x) = x e^x \newlinef′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=exx f(x) = \frac{e^x}{x} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of f(x) f(x) . \newline f(x)=e(x+1) f(x) = e^{(x + 1)} \newline f′(x)= f'\left(x\right) = ______
Get tutor helpright-arrow

Posted 7 months ago

Question
Find the derivative of f(x) f(x) . \newlinef(x)=x+3 f(x) = \sqrt{x+3} \newlinef′(x)= f'(x) = ______
Get tutor helpright-arrow

Posted 9 months ago

Question
Find the derivative of g(x) g(x). \newline g(x)=ln⁡(2x) g(x) = \ln(2x) \newline g′(x)= g^{\prime}(x) = ______
Get tutor helpright-arrow

Posted 10 months ago

View all (129)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant