SOLUTION: The gradient of the curve y = ax to the power 2 is equal to - 4 at the point where x=2. The value of a is......?

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Question 1125443: The gradient of the curve y = ax to the power 2 is equal to - 4 at the point where x=2. The value of a is......?
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the equation is y = ax^2.

when x = 2, y is equal to -4.

therefore -4 = a * 2^2 which becomes -4 = a * 4.

solve for a to get a = -4 / 4 = -1.

the equation becomes y = -1 * x^2 which is written as y = -x^2.

here's the graph.

$$$

the blue line is the graph of the equation.

the orange line is used to show the intersection of the graph with x = 2.

the intersection is the point (2,-4).

this says that the value of y is equal to -4 when the value of x is equal to 2.


Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

            I read and understand the problem differently from the tutor @Theo.

            Correspondingly,  my solution is different. 


The given function is  f(x) = .


Its gradient is the derivative  f'(x) = 2ax.


The value of the gradient at the point x= 2  is -4:  f'(2) = 2*a*2 = -4,


which implies  a= -1.


Answer.  The value of  "a"  is  -1.


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