Question

If f(x)=3x5−10x3+5, on what intervals is f″(x)>0?

Answer 1

Answer:

$(0.7937,\infty)$

Step-by-step explanation:

we are given an algebraic function in x, such that

$f(x) = 3x^5-10x^3+5$

To find when second derivative >0

For this let us find first and second derivative by successive differentiation.

$f(x) = 3x^5-10x^3+5\\f'(x) =15x^4-30x^2\\f'(x)=60x^3-30$

when ii derivative >0 we have

60x^3-30>0

$x^3>0.5\\x>0.7937$

f"(x)>0 in

$(0.7937,\infty)$