(a) Find the slope m of the tangent to the curve y = 4 + 4x^2 − 2x^3 at the point where x = a.
m = ___
(b) Find equations of the tangent lines at the points (1, 6) and (2, 4).
y(x) = ____ (at the point (1, 6))
y(x) = ____ (at the point (2, 4))
(c) Which is a graph of the curve and both tangents on a common screen.
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Verified answer
(a) y = 4 + 4x^2 - 2x^3
dy/dx = 8x - 6x^2
(dy/dx) at x=a , m = 8a - 6a^2