Thread: gradient function

can someone help with this question please

"the gradient function of y=ax^2 + bx + c is 4x+2. The function has a minimum value of 1. Find the values of a, b and c"

Originally Posted by 24680

can someone help with this question please

"the gradient function of y=ax^2 + bx + c is 4x+2. The function has a minimum value of 1. Find the values of a, b and c"

The gradient function is the derivative of y, so

dy/dx = 2 a x^2 + b = 4 x +2,

so we have a=2, b=2.

The minimum occurs where y'=4x+2=0, or where x=-1/2, and at -1/2

y(-1/2) = 1 - 1 + c = c,

but we are told that this minimum is 1, so c=1.

RonL