Math 124B Midterm 2 Winter 2023
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Math 124B
Midterm 2
Winter 2023
1. Compute the derivatives of the following functions. Do not simplify your answers.
(a) (4 points) 
(b) (4 points) 
(c) (5 points) 
(Give your answer in terms of x.)
2. Consider the curve given by the parametric equations
x = t2 − 6t
y = t − 3lnt
(a) (6 points) Find the equation of the tangent line to the curve when t = 1.
(b) (6 points) Find all times t ≥ 0 when the tangent line has slope equal to 1/3
3. (8 points) Each side of a square is increasing at a rate of 2 feet/second. At what rate is the area of the square increasing when the area of the square is 49 square feet?
4. (9 points) l.Find all the points (a, b) on the curve x2 + y3 − 6x = 18 where the tangent line is
5. (9 points) Let x2 − 6xy+y3 = 8. Find the value of y′′ at the point where x = 0.
2023-11-18