1) Find the equation of the line tangent to the graph of f(x) = (x² + 1)(x³ + 1) at the point where x = 1.

Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: 4) Find the derivative of f(x) = (5x² - 3)² in two different ways.

A:

Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: Find an equation of the line tangent to the graph of 3x G(x) = 4e ³x at the point (0,4).

A:

Q: f(x) = x3 + x + 6;    (−2, −4) (a) Find an equation of the tangent line to the graph of the…

A: f(x) = x3 + x + 6Recall the famous rule of differentiation: d(xn) / dx = nxn-1

Q: Find an equation of the line tangent to the graph of G(x) = 3e-² at the point (0, 3).

A: To find an equation of the line tangent to the graph of function G(x) = 3e-2x at the point (0,3).