Question

The derivative of the function f is given by f′(x)=−3x+4 for all x, and f(−1)=6. Which of the following is an equation of the line tangent to the graph of f at x=−1 ?

Answer 1

The equation of the line tangent to the graph of f at x = -1 is
`y = 7\cdot x +13`.

Explanation:

From Analytical Geometry we know that the tangent line is a first order polynomial, whose form is defined by:

`y = m\cdot x + b` (1)

Where:

`x` - Independent variable, dimensionless.

`y` - Dependent variable, dimensionless.

`m` - Slope, dimensionless.

`b` - Intercept, dimensionless.

The slope of the tangent line at
`x = -1` is:

`f'(x) = -3\cdot x +4` (2)

`f'(-1) = -3\cdot (-1) +4`

`f'(-1) = 7`

If we know that
`m = 7`,
`x = -1` and
`y = 6`, then the intercept of the equation of the line is:

`b = y-m\cdot x`

`b = 6-(7)\cdot (-1)`

`b = 13`

The equation of the line tangent to the graph of f at x = -1 is
`y = 7\cdot x +13`.