Is #f(x)=(x-4)(x-12)(x/4-1)# increasing or decreasing at #x=-1#?

1 Answer
Jul 8, 2017

#f(x)" is increasing at " x=-1#

Explanation:

#"to determine if f(x) is increasing/decreasing at x = a"#
#"differentiate and evaluate " f'(x) " at "x = a"#

#• " if " f'(a)>0" then f(x) is increasing at x = a"#

#• " if " f'(a)<0" then f(x) is decreasing at x = a"#

#"expand factors of f(x)"#

#f(x)=(x^2-16x+48)(x/4-1)#

#color(white)(f(x))=1/4x^3-5x^2+28x-48#

#"differentiate using the "color(blue)"power rule"#

#f'(x)=3/4x^2-10x+28#

#f'(-1)=3/4+10+28>0#

#rArrf(x)" is increasing at x = - 1"#