Find an equation for the tangent line to the curve y = x⁴ - 11 at (2, 5). A) y = 32x B) y = 32x - 11 C) y = 32x³ - 59 D) y = 32x - 59 E) y = 32x³ - 11

Question

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function at the point (2,5) and then use the point-slope form of the equation of a line. Taking the derivative of y with respect to x, we get: y' = ⁴ Substituting x = 2 in the expression above, we get y'(2) = ⁴ y'(2) = 32 This is the slope of the tangent line. Using the point-slope form of the equation of a line, we get: y - 5 = 32(x - 2) Simplifying this equation, we get: y = 32x - 59 Therefore, the answer is D.

Find an Equation for the Tangent Line to the Curve