Question

Find the value of k when a curve has the equation y=x²−kx²+5. When x=4, the gradient of the curve is 5.

A) 0.25
B) 0.5
C) 1
D) 1.5
E) 2

Answer 1

To find the value of k when a curve has the equation y=x²−kx²+5, we need to determine the value of k that makes the gradient of the curve equal to 5 when x=4. By taking the derivative of the equation and substituting the given value of x, we can solve for k. The value of k is A)0.25.

Step-by-step explanation:

To find the value of k when a curve has the equation y=x²−kx²+5, we need to determine the value of k that makes the gradient of the curve equal to 5 when x=4.

The gradient of a curve at a given point is equal to the derivative of the curve at that point. So, to find the gradient of the curve at x=4, we need to take the derivative of the equation with respect to x and then substitute x=4.

Taking the derivative of the equation y=x²−kx²+5 with respect to x gives dy/dx = 2x - 2kx. Substituting x=4, we get dy/dx = 2(4) - 2k(4) = 8 - 8k.

Given that the gradient is 5, we have 8 - 8k = 5. Solving for k, we find that k = 0.25. So the answer is option A) 0.25.