(2, 0): = 6x − 6, which is 6 at (2, 0). Since this is the slope of the tangent line, and the
slope of the normal line is the opposite reciprocal, the slope of the normal line is − . Plug this
information into the point-slope formula of a line and simplify to slope-intercept form: y − 0 =
− (x − 2) or y = − x + .
- D Either use L’Hôpital’s rule or recall that and = 1. In this case,
can be rewritten as = 1 1 = 1.
- C Following the Second Fundamental Theorem of Calculus,
(2 − t^2 ) dt = [2 − (x^3 )^2 ](3x^2 ) = (2 − x^6 )(3x^2 ) = 6x^2 − 3x^8.
- A Use u-substitution and recognize that the solution will be an inverse sine function.
= = . Thus, the final solution is: sin−1 + C
- D f′(x) = 3x^2 + 2 and f′ (1) = 5.
- D Whenever we have a polynomial where the x’s and y’s are not easily separated, we need to use
implicit differentiation to find the derivative.
Step 1: Take the derivative of everything with respect to x.
Remember that = 1!
Step 2: Simplify, and then put all of the terms containing on one side, and all of the other
terms on the other side.
