Q. 155.0( 1 Vote )

Determine for wha

Answer :

Given,




Now put f(x) = 0,




3x6 – 3 = 0


x6 – 1 = 0


x6 = 1


Therefore, above equation has only two solutions


x = 1 and x = -1


For x < -1 and x > 1


Put x = 2, we have



And for x (-1, 1)\{0}


Put x = 1/2



Now, As f’(x) < 0 in (-1, 1)\{0}, f(x) is strictly decreasing in (-1, 1)\{0}


And as f(x) > 0 in (-∞, -1) (1, ∞), f(x) is strictly increasing in (-∞, -1) (1, ∞)


OR


We know, derivative of a function at any point gives the slope of tangent at that point.


Now, given tangent


y = x – 11


comparing with, y = mx + c


we get, m = 1 (slope)


Now,



For, m = 1



1 = 3x2 – 11


3x2= 12


x2 = 4


x = ± 2


When x = 2


y = x – 11 = 2 – 11 = -9


When x = -2


y = x – 11 = -2 – 11 = -13


Therefore, possible points are (2, -9) and (-2, -13)


Now, equation of curve y = x3 – 11x + 5


At x = 2


y = (2)3 – 11(2) + 5 = -9


(2, -9) satisfy the curve equation


At x = -2


y = (-2)3 – 11(-2) + 5


y = -8 + 22 + 5 = 19


(-2, -13) doesn’t satisfy the equation


(2, -9) is the required point!


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the equationRD Sharma - Volume 1

Find the equationMathematics - Board Papers

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the equationRD Sharma - Volume 1

Find the conditioMathematics - Exemplar