derivative of this curve is zero. Take the derivative.
= 6x^2 − 6x − 12Set it equal to zero and solve for x. Get accustomed to doing this: It’s one of the most common questions
in differential calculus.
= 6x^2 − 6x − 12 = 06(x^2 − x − 2) = 06(x − 2)(x + 1) = 0x = 2 or x = −1Third, find the y-coordinates of these two points.
y = 2(8) − 3(4) −12(2) + 20 = 0y = 2(−1) − 3(1) − 12(−1) + 20 = 27Therefore, the points are (2, 0) and (−1, 27).
PRACTICE PROBLEM SET 8
Now try these problems. The answers are in Chapter 19.
1.Find the equation of the tangent to the graph of y = 3x^2 − x at x = 1.2.Find the equation of the tangent to the graph of y = x^3 − 3x at x = 3.3.Find the equation of the tangent to the graph of y = at x = 3.4.Find the equation of the normal to the graph of y = at x = 4.5.Find the equation of the tangent to the graph of y = 2x^3 − 3x^2 − 12x + 20 at x = 2.6.Find the equation of the tangent to the graph of y = at x = 5.