Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Find a value of c such that the conclusion of the mean value theorem is satisfied for
f(x) = -2x 3 + 6x - 2
f(x) is a polynomial function and is continuous and differentiable for all real numbers. Let us evalute f(x) at x = -2 and x = 2 f(-2) = -2(-2) 3 + 6(-2) - 2 = 2 f(2) = -2(2) 3 + 6(2) - 2 = - 6
Evaluate [f(b) - f(a)] / (b - a) [f(b) - f(a)] / (b - a) = [ -6 - 2 ] / (2 - -2) = -2
Let us now find f '(x). f '(x) = -6x 2 + 6
We now construct an equation based on f '(c) = [f(b) - f(a)] / (b - a) -6c 2 + 6 = -2
Solve for c to obtain 2 solutions c = 2 sqrt(2/3) and c = - 2 sqrt(2/3)
Below is shown the graph of f, a secant and the two tangent corresponding to the two solutions found. The secant and the two tangents are parallel since their slopes are equal according to the mean value theorem.
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Win Gift vouchers upto Rs 500/-
Register Yourself for a FREE Demo Class by Top IITians & Medical Experts Today !