Find the derivative and interval values f(x) = 3/x + 4 Squareroot x^3, f\'(1) g(

Question

Find the derivative and interval values f(x) = 3/x + 4 Squareroot x^3, f'(1) g(t) = 9t^2 sin t, g'(pi) h(z) = 3z^2 + 7z - 10/z^2, h'(2) p(w) = 4w^4 - 8w^2, p'(-1) W(y) = 3 cos y - 7 sin y + 8y, w'(0) B. Solve the given equation f(x) = x^2 + 7x + 1, f'(x) = 21 g(x) = x^3 + 4x^2, g'(x) = -5 y(x) = x + 4/xc, y'(x) = 0 C. Miscellaneous Write an equation of the tangent to the graph of f(x) = 2x + 4x at (-1, f(-1)) (2, f(2)) Determine the points on the graph of y = x^3 - 3x + 6 where the tangent is horizontal

Explanation / Answer

1.y= f(x)= 3/x + 4sqrt(x^3)

dy/dx= d(3/x)/dx + d(4sqrtx^3)/dx

dy/dx= -3/x^2 + 6x2/sqrt(x^3)

f'(1)= -3 + 6= 3

2. y=g(t)=9t^2 sin t

dy/dt=9t^2 d(sin t)/dt + sin t d(9t^2)/dt = 9t^2 cos t + 18t sin t

g'(pi)= -9pi^2

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