Question

For the function f(x) = -4x^2 + 8x+8, find the slope of the tangent line at
X = -3.

Answer 1

Find the corresponding y-value to x=−3.

Substitute −3 in for x.

y=−4(−3)²+8(−3)+8

Simplify −4(−3)²+8(−3)+8

y=−36−24+8 => y=−52

Find the first derivative and evaluate at x=−3 and y=−52 to find the slope of the tangent line.

Plug the slope and point values into the point-slope formula and solve for y

y=32x+44

Explanation: