If the gradient of the curve y = 2kx2 + x + 1 at x = 1 is 9, find k.
Question 1 Report
If the gradient of the curve y = 2kx2 + x + 1 at x = 1 is 9, find k.
Answer Details
The given curve is y = 2kx² + x + 1, and we are asked to find the value of k when the gradient at x = 1 is 9.
The gradient of a curve at a particular point is the slope of the tangent to the curve at that point. To find the gradient of this curve at x = 1, we need to differentiate it with respect to x:
dy/dx = 4kx + 1
Now we can substitute x = 1 and set the result equal to 9, which gives:
4k(1) + 1 = 9
Simplifying this equation, we get:
4k = 8
Dividing both sides by 4, we obtain:
k = 2
Therefore, the value of k that satisfies the given conditions is 2.
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