Pangasinan State University
Urdaneta City Campus
College of Engineering and Architecture
1ST SEMESTER 2023-2024
MATH 102 – DIFFERENTIAL CALCULUS
TANGENTS & NORMAL TO PLANE CURVES INCREASING & DECREASING FUNCTIONS &
SKETCHING OF POLYNOMIAL CURVES
COURSE
PS NO-MT-04
Instructions: Solve the following problems as instructed. Show your
solutions. No solutions wrong.
S
1. Determine the equations of the tangent and normal lines to the
curve 𝑦 = 𝑥 2 − 2𝑥 at its intersection with the line 𝑦 = 3.
AM
O
2. Determine the equations of the tangent and normal lines to the
curve 2𝑥𝑦 + 5𝑥 − 3𝑦 = 0 at 𝑥 = 4.
R
3. Determine the equations of the tangent lines to the curve 𝑥 2 +
4𝑦 2 = 8 parallel to the line 𝑥 + 2𝑦 = 6.
YN
O
N
4. Locate critical points to the curve 𝑦 = 𝑥 3 − 3𝑥 2 − 9𝑥 + 20 and
determine maxima and minima using the first and second
derivative test.
R
E
5. Locate critical points to the curve 𝑦 = (𝑥 − 4)4 (𝑥 + 3)3 and
determine maxima and minima using the first and second
derivative test.
G
R
6. Determine the coefficients of the curve 𝑦 = 𝑎𝑥 4 + 𝑏𝑥 3 + 𝑐𝑥 2 + 𝑑 𝑥 + 𝑒
pass through the point (1, −9) and have critical points at (0,0)
and (−1, −1).
E
N
7. Sketch the curve 𝑦 = 𝑥 3 + 3𝑥 2 + 3𝑥 using a suitable scale
indicating all relevant points.
8. Sketch the curve 4𝑦 = 20𝑥 3 − 3𝑥 5 using a suitable scale
indicating all relevant points.
9. Sketch the curve 𝑦 = 𝑥 4 − 6𝑥 2 − 7 using a suitable scale
indicating all relevant points.
Prepared by:
Engr. Reyno N. Ramos
Instructor
Noted by:
Engr. Mark Jefferson B. Castro
Department Chair