Question

(b) 90 n cms
(C) 85 a cm/s
(D) 89 T CILS
Find points at which the tangent to the curve y =X3 - 3x2 – 9x + 7 is parallel to the x-axis
(A) (3,-20) and (-1, 12) (B) (3,20) and (1, 12) (C) (3,-10) and (1, 12) (D) None of the
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Answer 1

Answer:

The main point is when any curve is parallel to x axis

then its slope is zero

Step-by-step explanation:

Here, y = x³ - 3x² - 9x + 7

differentiate y with respect to x

dy/dx = 3x² - 6x - 9

put dy/dx = 0 ∵( because slope of tangent , dy/dx is parallel to the x-axis )

so, 3x² - 6x - 9 = 0

=> x² - 2x - 3 = 0

=> x² - 3x + x - 3 = 0

=> x(x - 3) + 1(x - 3) = 0

=> x = -1 , 3

at x = -1 , y = (-1)³ - 3.(-1)² - 9.(-1) + 7 = 12

at x = 3 , y = 3³ - 3.3² - 9.3 + 7 = -20

hence, required points are (-1,12) and (3,-20)