|Let f(0) = 3 and f'(0) = 2. Then the equation of the tangent line to the graph of y = f(x) at x = 0 is y =

Q: f(3) = -9 and f'(3) = 7 . Then the equation of the tangent line to the graph of y = f(x) at x = 3 is

A: Given Data: The value of function at x=3 is: f(3)=-9 The value of the derivative of the function at…

Q: Find the equation of the tangent line to the curve f(x)= x2 +5x when x=1.

A:

Q: Find the slope of the tangent line at the point P = (1, 1) on the graph of              ex-y = 2x2 -…

A: Given,          ex-y = 2x2- y2    at   P=(1, 1)

Q: Find the equation of the tangent line to the curve f(x) = x* - 9x2 + 2 at the point x=1.

A:

Q: 3 =-=—= x³. - 4x² + 16x + 14 with tangent lines parallel to the line 20x - 5y = 2. Find all points…

A:

Q: Find the derivative of the function

A: Given:y=arctanx+x1+x2Differentiate formula:ddxarc tanx=11+x2ddxuv=vdudx-udvdxv2

Q: Find the derivative of the function y= arctan x +x/1+x2

A:

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

A:

Q: 4) Determine the equation of the tangent line to the function 2 f(x) = x at the point (3, 9).

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: