Find the derivative of the given function. (X2 + 2)3 6x5 + 20x3 + 24x 6x5 + 12x3

Question

Find the derivative of the given function. (X2 + 2)3 6x5 + 20x3 + 24x 6x5 + 12x3 + 12x 3x5 + 24x3 + 24X 6x5 + 24x3 + 24x Find the slope of the line tangent to the graph of the function at the given value of x. y= 9x5/2 _ 7x3/2; x = 4 6 96 159 8 Find an equation for the line tangent to given curve at the given value of x. y = x2 - x at x = -3 y = -7x + 6 y = -7x + 9 y = -7x-9 y = -7x-6 find all values of x (if any) where the tangent line to the graph of the function is horizontal. y = x3 + 4x2 - 256x + 32 -32 / 3, 8 -32/3, 32/3, 8 8 32/3, -8 the following. At what points on the graph of f(x) = 2x3 - 3x2 - 74x is the slope of the tangent line -2? (0, 0), (4, -216) (-3,141), (4, -216) (3, -195), (141,120) ("3,141), (1, -75) the product rule to find the derivative. f(x) = (5x3 + 4)(3x7 - 5) f(x) = 150x9 + 84x6 - 75x f(x) = 150x9 + 84x6 - 75x2 f(x) = 20x9 + 84x6 -75x f(x) = 20x9 + 84x6 - 75x2

Explanation / Answer

17). y = 9x^(5/2) - 7x^(3/2) or, y' = 9(5/2) x^(3/2) - 7(3/2)x^(1/2) at x = 4 : or, y' = (45/2) (8) - (21/2) (2) or, y' = 180 - 21 or, y' = 159 (C) 19). y = x^3 + 4x^2 - 256x + 32 or, y' = 3x^2 + 8x - 256 = 0 or, (3x + 32 )(x - 8) = 0 or, x = -32/3 , 8 (A) 20) y = 2x^3 - 3x^2 - 74x or, y' = 6x^2 - 6x - 74 = -2 or, 6x^2 - 6x - 72 = 0 or, 3x^2 - 3x - 36 = 0 or, (3x + 9)(x - 4) = 0 or, x = -3 , x = 4 (B) Answer

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