Saturday

December 20, 2014

December 20, 2014

Posted by **amir** on Sunday, March 4, 2012 at 9:51pm.

- calculus -
**MathMate**, Sunday, March 4, 2012 at 11:53pmTo find if f(x) is concave up, we calculate the sign f"(x).

The interval on which f"(x)>0 is concave up, and vice versa.

Let f(x)=cos²(x),

f'(x)=-2sin(x)cos(x)

f"(x)=-2cos(2x)

Now plot f"(x) between 0 and 2π to get:

f"(x)≥0 for x∈[-π/4,π/4]

f"(x)≤0 for x∈[π/4,3π/4]

f"(x)≥0 for x∈[3π/4,5π/4]

f"(x)≤0 for x∈[5π/4,7π/4]

...

Can you take it from here?

**Answer this Question**

**Related Questions**

Calculus - THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on ...

calculus - Let f (x) = x3 ��3x2 +5x+2. Find the open intervals on ...

calculus - Let f (x) =7x-5/x+3 . Find the open intervals on which f is concave ...

calculus - Let f (x) = x^2 + 5x-14. Find the open intervals on which f is ...

Calculus - Suppose you know that f(x) is an odd functon on the domain of all ...

Calculus - f(x)=[3x^13]e^(−7x) On which intervals is the function concave ...

calculus - If f(x) = 3 cos^2(x) − 6 sin(x) 0 ≤ x ≤ 2π ...

calculus - Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. a) Determine where...

Calculus - Consider the function f(x)=xe^2x. Find the intervals on which f(x) is...

calculus - Please help me solve. I think increase = concave up and decrease = ...