Basic Differentiation

1. Nov 19, 2007

DizzyDoo

[SOLVED] Basic Differentiation

Hi there, I've heard that this forum is the best for getting some quick help.

Find the gradient of the tangent to the curve at the given point:
y = 2x² + 3x + 5 when x = -1

2. Relevant equations
Right, I'm very new a this, but dy/dx is the way to go right?

3. The attempt at a solution:
y = 2x² + 3x + 5 when x = -1
dy/dx it, and I get:
dy/dx=4x + 3
Substitute -1 in and I get
y=-1

So I've now got two points; (-1,-1) but thats not the gradient, but I've got the feeling I'm half way there. Any help would be great thanks!

2. Nov 19, 2007

HallsofIvy

Staff Emeritus
Well, first of all (-1, -1) is ONE point, not two! But more important, if dy/dx= 4x+ 3, then putting x=-1 gives you dy/dx= -1, not y. At first I thought that it was a typo but then you say "that's not the gradient". It certainly IS the gradient! You are not "half way there", you are completely there!

(It is true that, if x=-1, y= 2(-1)2+ 3(-1)+ 5= 2- 3+ 5= 4. y= 4 so the graph of the function passes through the point (-1, 4). The tangent line to the curve is y= -1(x+1)+ 4 or y= -x+ 3.)

3. Nov 20, 2007

DizzyDoo

Fantastic, I can finish off the rest of the questions now. Thanks!