AP Calculus AB Practice Set 3

Find y’ given that y=3\left(x-4\right)^2-2 .

Evaluate the Integral I = \int{\frac{18}{t\left(t^6-3\right)}dt} .

Find the derivative of the function f(t).

f(t) = \frac{t^4+1}{\left(t^4-1\right)^6}

Use the Trapezoidal Rule to approximate the area under the curve of the differentiable function f\left(x\right) on the interval \left[1,\ 5\right] with n=4,\ as given in the table below:

If f\left(x\right)=cos\left(x^2-\pi\right) , then f\prime\left(\sqrt{\frac{\pi}{2}}\right) .

Find the average rate of change of the function f\left(x\right)=x^2+5x from x_1=3 to x_2=8 .

If \int_{0}^{6}f\left(x\right)dx=10,\ \int_{3}^{0}g\left(x\right)dx=-5 , and \int_{3}^{6}f\left(x\right)dx=6 . Find the value of \int_{0}^{3}\left(2f\left(x\right)+5g\left(x\right)\right)dx .

Determine the equation of the tangent line to the function x^7+x^5y^4=0 at point (-1, -1) in the form y = mx + b.

Determine the area enclosed by the curves represented by the provided equations.

y=2x^2-4x+4;\ y=x^2+6x-5

Evaluate the definite integral: \int_{-\infty}^{0}{\frac{z}{z^4+16}dz} .