Copyright

Given {eq}f''(x) = 6x -2 {/eq} and {eq}f'(-1) = 3 {/eq} and {eq}f(-1) = -4 {/eq}. Find {eq}f'(x) {/eq} and {eq}f(3) {/eq}.

Question:

Given {eq}f''(x) = 6x -2 {/eq} and {eq}f'(-1) = 3 {/eq} and {eq}f(-1) = -4 {/eq}. Find {eq}f'(x) {/eq} and {eq}f(3) {/eq}.

Derivative's Solution:

If the second derivative function is given, then we'll get the two constant of integration C (constant for first derivative function) and D (constant for original function) respectively so we'll compute these constants using initial values.

{eq}\begin{align*} \displaystyle \int f''(x)\ dx&=f'(x)+C\\ \displaystyle \int( f'(x)+C)\ dx&=f(x)+Cx+D\\ \end{align*} {/eq}

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer


We are given:

The second derivative function and initial values are:

{eq}f''(x) = 6x -2\\ f'(-1) = 3\\ f(-1) = -4 {/eq}

Simplifying the...

See full answer below.


Learn more about this topic:

Loading...
Indefinite Integrals as Anti Derivatives

from

Chapter 12 / Lesson 11
6.1K

Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.


Related to this Question

Explore our homework questions and answers library