I had this question today- Find the gradient from x = -5 to x = -4 of y = -x^(3) + 1.

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JohhnyJOhhny

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I dont even know where to start. I know the derivative of the equation is -3x^2 but that's all I got. Any hints?
 
average rate of change ...

[MATH]\dfrac{y(b)-y(a)}{b-a}[/MATH]
 
If you put -5 into -3x^2, you get -75. I think you forgot to square it.
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Anyway, because you are finding the gradient between two points on the curve, you need to use the original equation, not the derivative. So the point (-5, -124) is one point. Find the other and then the gradient between them.

Remember, the derivative gives you a "rule" for working out the tangent at one given point. That's not want you are asked for here.
 
Harry_the_cat said:
If you put -5 into -3x^2, you get -75. I think you forgot to square it.
...
Anyway, because you are finding the gradient between two points on the curve, you need to use the original equation, not the derivative. So the point (-5, -124) is one point. Find the other and then the gradient between them.

Remember, the derivative gives you a "rule" for working out the tangent at one given point. That's not want you are asked for here.
Click to expand...
For the two points I got (-5, 126) and (-4, 64). I used the formula and then got -61. (I think you forgot the negative)
 
[MATH]y=1-x^3[/MATH]
[MATH]\dfrac{y(-4) - y(-5)}{-4-(-5)} = \dfrac{(1+64)-(1+125)}{1} = -61[/MATH]
 
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