quick question: gradient of Y = 2X^3 + 5X^2 – 4X at x = 1/2

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12345678

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quick question: gradient of Y = 2X^3 + 5X^2 – 4X at x = 1/2

Hello, I was wondering if somebody could help me find the gradient given this scenario:
Equation of curve; Y = 2X^3 + 5X^2 – 4X
I need to find the gradient when X = ½

So my thinking was to differentiate;
Dy/dx = 6X^2 + 5X – 4
I was then thinking to substitute X = ½ into dy/dx;
6(1/2)^2 + 5(1/2) – 4
= 6/4 + 5/2 – 4
= 0
So is the gradient 5/2 or can you only find this when the form is y=mx+c or 0?
Any help will be appreciatedJ

 
12345678 said:
Hello, I was wondering if somebody could help me find the gradient given this scenario:
Equation of curve; Y = 2X^3 + 5X^2 – 4X
I need to find the gradient when X = ½

So my thinking was to differentiate;
Dy/dx = 6X^2 + 5X – 4
I was then thinking to substitute X = ½ into dy/dx;
6(1/2)^2 + 5(1/2) – 4
= 6/4 + 5/2 – 4
= 0
So is the gradient 5/2 or can you only find this when the form is y=mx+c or 0?
Any help will be appreciatedJ
Click to expand...

What is the definition of the gradient of a curve?
 
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