Friday

December 19, 2014

December 19, 2014

Posted by **Eric** on Wednesday, May 15, 2013 at 10:50am.

f(x)= definite integral sign where a=0 and b=x.

t^2-4/(1+(cos^2(t)) dt

what should my value for u be? is it just t. not sure how to even tackle this problem.

- calculus-extrema -
**Steve**, Wednesday, May 15, 2013 at 10:53amThe clue here is that we want to find extrema of f(x), which involves finding the derivative of f. Since f(x) is defined as an integral, we don't really have to do the integration. We just apply the rules for differentiating under the integral sign. (See wikipedia, and scroll down for some examples)

f(x) = ∫[0,x] (t^2-4)/(1+(cos^2(t)) dt

so,

df/dx = (x^2-4)/(1+cos^2 x)

So, f'=0 when x^2-4 = 0, since the bottom is never zero.

Obviously the extrema are at x=2,-2.

- calculus-extrema -
**Eric**, Wednesday, May 15, 2013 at 10:59amThank you!

**Answer this Question**

**Related Questions**

Extrema-Calc - Find and classify the relative maxima and minima of this function...

Followup-Calculus-Extrema - Find and classify the relative maxima and minima of ...

Extrema-Check my work please? - Find and classify the relative maxima and minima...

Minima Maxima - Find and classify the relative maxima and minima of f(x) if f(x...

Calculus - Find and classify the relative maxima and minima of f(x) if f(x)= ...

calculus - If g is a differentiable function such that g(x) is less than 0 for ...

Calculus - Q: If y=sinx/(1+tanx), find value of x not greater than pi, ...

differentiability - If g is a differentiable function such that g(x) is less ...

Calculus - Find the local extrema of the function f(x) = (e^x^2+1)/(2x+1) ...

PLIZ VERY URGENT - Use implicit differentiation to show that a function defined ...