Question
What is the gradient at the point(3,35) for the function y=x²+7x+5
Answers
GPT 3.5
To find the gradient at a specific point on a curve, you need to find the derivative of the function and then evaluate it at that point.
Given function: y = x² + 7x + 5
To find the derivative of the function, we differentiate it with respect to x:
dy/dx = d/dx(x²) + d/dx(7x) + d/dx(5)
dy/dx = 2x + 7
Now, we can evaluate the derivative dy/dx at the point (3, 35):
dy/dx = 2(3) + 7
dy/dx = 6 + 7
dy/dx = 13
Therefore, the gradient at the point (3, 35) for the function y = x² + 7x + 5 is 13.
Given function: y = x² + 7x + 5
To find the derivative of the function, we differentiate it with respect to x:
dy/dx = d/dx(x²) + d/dx(7x) + d/dx(5)
dy/dx = 2x + 7
Now, we can evaluate the derivative dy/dx at the point (3, 35):
dy/dx = 2(3) + 7
dy/dx = 6 + 7
dy/dx = 13
Therefore, the gradient at the point (3, 35) for the function y = x² + 7x + 5 is 13.