Gradient of the curve

[IloveManUtd]

The gradient of the curve y= ax[sup:8lu77rre]2[/sup:8lu77rre] + bx at the points x=1 and x=3 are -2 and 10 respectively. Find the values of a and b

Do I subsitute the values of x given to create 2 simultaneous equations or do I differentiate the equation first. HELP PLEASE!

 

[mmm4444bot]

The gradient of the curve y= ax[sup:yox1a7lt]2[/sup:yox1a7lt] + bx at the points x=1 and x=3 are -2 and 10 respectively. Find the values of a and b

Do I subsitute the values of x given to create 2 simultaneous equations Yes, but substitute them into the derivative.

do I differentiate the equation first. Yes. You need the derivative first, before you substitute.

Did you try anything?

Look what happens, when we substitute the given values for x into the given expression for y:

y = a + b

y = 9a + 3b

How can we solve this system for a and b ? We can't ! They did not give us the corresponding values of y.

(If you had done this, perhaps you would have tried using the derivative, instead.)

We do know the corresponding values for y` (the derivative of y).

y` = -2 when x = 1

y` = 10 when x = 3

Please show your work, if you need more help with this exercise.

Thank you for asking specific questions, and don't be timid to TRY stuff.