Thread: Curve Sketching

Let f(x) = ax3 + bx2 + cx + 1. Determine the values of a,b, and c so that f(x) has a point of inflection at x = 2, a local minimum at x = -2, and f(1) = 2.

So, f'(x) = 3ax2 + 2bx + c
f"(x) = 6ax + 2b

I know that f'(x) = 0 when x = -2 so: 12a - 4b + c = 0
and f"(x) = 0 when x = 2 so: 6a + b = 0
and a + b + c = 1 since f(1) = 2

I'm not sure if i'm going in the right direction with this question but i'm stuck at this point. Any help would be appreciated.

Originally Posted by steezin

Let f(x) = ax3 + bx2 + cx + 1. Determine the values of a,b, and c so that f(x) has a point of inflection at x = 2, a local minimum at x = -2, and f(1) = 2.

So, f'(x) = 3ax2 + 2bx + c
f"(x) = 6ax + 2b

I know that f'(x) = 0 when x = -2 so: 12a - 4b + c = 0
and f"(x) = 0 when x = 2 so: 6a + b = 0
and a + b + c = 1 since f(1) = 2

I'm not sure if i'm going in the right direction with this question but i'm stuck at this point. Any help would be appreciated.

solve the system of equations ...







subtract the 3rd equation from the 1st ...



from the 2nd equation ...









yes, I know ... some ugly coefficients.