A curve is defined for x > 0. The gradient of the curve at the point (x,y) is given by dy/dx = x^(3/2)-2x. Show that this curve has a minimum point and find it.

This is a typical exam style question, taken from an AQA paper. This question is testing your knowledge of stationary points and differentiation. Step 1: Find all stationary points by setting the first derivate to 0, and solving the equation. Step 2: Determine what type of stationary points those we found in step 1 are. This is done by obtaining the second derivative, and substituting in the x values found in step 1. (Optional step 3: interpretationFirst derivative - gradientSecond derivative - rate of change of gradient)

YC
Answered by Yishuang C. Maths tutor

4225 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Using the Trapezium rule with four ordinates (three strips), estimate to 4 significant figures the integral from 1 to 4 of (x^3+12)/4sqrt(x). Calculate the exact value of this integral, comparing it with your estimate. How could the estimate be improved?


Sketch the curve y = (x^2 - 9)(x - 2)


How do I find a stationary point? And how do I determine whether it is a maximum or minimum point?


Find f'(x) and f''(x) when f(x) = 3x^2 +7x - 3


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences