Chapter 4: Q. 1 (page 364)

Find a function f that has the given derivative f' and value f(c), if possible.
$f' (x) = x^{8} - x^{2} + 1, f (0) = - 1$

Short Answer

Expert verified

The function is this $\frac{x^{9}}{9} - \frac{x^{3}}{3} + x + c$

and value of f(-1)= $\frac{- 20}{9}$

Step by step solution

Step 1.Given

The given function is $f' (x) = x^{8} - x^{2} + 1, f (0) = - 1$

Step 2. Finding the function using integration

$Integrating both sides with respect to x, \int f' (x) = \int x^{8} - x^{2} + 1 d x = \frac{x^{9}}{9} - \frac{x^{3}}{3} + x + c where c is constant$

Step 3. Finding the value of f(c).

$w h e n f (0) = - 1 f (x) = \frac{x^{9}}{9} - \frac{x^{3}}{3} + x + c f (0) = 0 - 0 + 0 + c - 1 = c f (c) = f (- 1) = \frac{{(- 1)}^{9}}{9} - \frac{{(- 1)}^{3}}{3} + (- 1) + - 1 = \frac{1}{9} - \frac{1}{3} - 1 - 1 = \frac{- 2}{9} - 2 = \frac{- 20}{9}$

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Find a function f that has the given derivative f' and value f(c), if possible.
$f' (x) = x^{8} - x^{2} + 1, f (0) = - 1$

Short Answer

Step by step solution

Step 1.Given

Step 2. Finding the function using integration

Step 3. Finding the value of f(c).

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Find a function f that has the given derivative f' and value f(c), if possible.f'(x)=x8−x2+1,f(0)=−1

Short Answer

Step by step solution

Step 1.Given

Step 2. Finding the function using integration

Step 3. Finding the value of f(c).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

Find a function f that has the given derivative f' and value f(c), if possible.
$f' (x) = x^{8} - x^{2} + 1, f (0) = - 1$