MAT 1330 Midterm: Midterm 2

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

ool Careruly. maRe sure you are answering the que correctly I) y =x" + 2x Find where the slope of a tangent line is equal to 3 2) Differentiate each of the following functions a) y =-6x-4 2) Determine if the function has any horizontal tangent lines b) g(x)-re2x c) y=x2/3-74/3 3 24X 2 r +1 2 y = 2-x3 3) Use the quotient rule to show that the derivative of y = sec θ is y' = sec θ tan θ 4) Find the derivative only three of the following functions. Simplify each answer as mu possible a) f(x)=x' cos x b) f(x)= b) f(x)= 4x-21 y=ln(x5) c) -7 4t +5 e)y3x21 f) g(x)=cos(x3+4)