Find the value of C' for which the tangent line to the graph of the function f(x) = 2e at the point (0, 2) is the same as the tangent line to the curve (x + 1)² + (y - 3)² = 2 at the same point. Justify your answer.

Q: The graph of y = xln x has one horizontal tangent line. Find an equation for it.

A: Given: y=xlnx We know that if a functiony=fx have horizontal tangent line then slopem of tangent is…

Q: Find the second derivative of the function y=4√x+1.

A:

Q: Find the slope of the graph of the function x2+y2=xy+1/4 at (1/2 , 1/2)

A: Given function is Differentiating both sides with respect to x, we get

Q: Find the equation of the tangent line to the graph of f(x) = x² - 5 at the point (3, 4).

A: We have to find the equation of tangent of the graph f(x)=x2-5 at the point (3,4).