# Is #f(x)=4x^5-x^4-9x^3+5x^2-7x# concave or convex at #x=-1#?

##### 1 Answer

May 11, 2016

concave at x = -1

#### Explanation:

To determine if a function is concave/convex we calculate the value of f''(x) at x = a.

• If f''(a) > 0 , then f(x) is convex at x = a

• If f''(a) < 0 , then f(x) is concave at x = a

#f(x)=4x^5-x^4-9x^3+5x^2-7x# differentiate using the

#color(blue)" power rule"#

#rArrf'(x)=20x^4-4x^3-27x^2+10x-7# and

#f''(x)=80x^3-12x^2-54x+10# so

#f''(-1)=80(-1)^3-12(-1)^2-54(-1)+10#

#=-80-12+54+10=-28# Since f''(-1) < 0 , then f(x) is concave at x = -1

graph{4x^5-x^4-9x^3+5x^2-7x [-36.52, 36.53, -18.24, 18.29]}