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

Answer:

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

Step-by-step 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 $y = 7\cdot x +13$.