Question

Is `f(x)=(x-1)^2+2x^2-3x` increasing or decreasing at `x=-1`?

Answer 1

Decreasing

Explanation:

To find if the function is increasing / decreasing at x = -1

differentiate to obtain f'(x) and test it's value at x = -1

• If f'(x) > 0 then f(x) is increasing

• If f'(x) < 0 then f(x) is decreasing

f(x) = `(x - 1 )^2 + 2x ^2 - 3x`

( multiply out brackets an collect like terms )

f(x) `= x^2 - 2x + 1 + 2x^2 - 3x = 3x^2 - 5x + 1`

hence f'(x) = 6x - 5

and f'(-1 ) = - 11 < 0 and so f(x) is decreasing.

graph{3x^2 -5x+1 [-14.05, 14.05, -7.02, 7.03]}