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

4344 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrate a^x with respect to x


Evaluate the integral between 5 and 3 for xe^x


How do you find and solve a composite function?


The equation of a line is y=3x – x^3 a) Find the coordinates of the stationary points in this curve, stating whether they are maximum or minimum points b) Find the gradient of a tangent to that curve at the point (2,4)


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences