2. Intro to Derivatives

Derivatives and tangent lines

a. For the following functions and values of a, find f′(a).

f(x) = 1/ x²; a= 1

Derivatives and tangent lines

a. For the following functions and values of a, find f′(a).

f(x) = √2x+1; a= 4

Derivatives and tangent lines

a. For the following functions and values of a, find f′(a).

f(x) = √3x; a= 12

Derivatives and tangent lines

b. Determine an equation of the line tangent to the graph of f at the point (a,f(a)) for the given value of a.

f(x) = √3x; a= 12

Derivatives and tangent lines

a. For the following functions and values of a, find f′(a).

f(x) = 1/3x-1; a= 2

Derivatives and tangent lines

b. Determine an equation of the line tangent to the graph of f at the point (a,f(a)) for the given value of a.

f(x) = 1/3x-1; a= 2

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = 2x + 1; P(0,1)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = -7x; P(-1,7)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = 3x² - 4x; P(1, -1)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = 8 - 2x²; P(0, 8)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = x² - 4; P(2, 0)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = 1/x; P (1,1)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = x³; P (1,1)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x)= 1/(2x + 1); P (0,1)

Use definition (2) (p. 135) to find the slope of the line tangent to the graph of f at P.

f(x) = √(x - 1); P (2,1)