Question

I need help with this

Answer 1

Using derivatives, it is found that regarding the tangent line to the function, we have that:

• The slope is of 962.

• The equation of the line is y = 962x - 5119.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:

f(x) = 5x³ + 2x + 1.

The derivative is given by:

f'(x) = 15x² + 2.

Hence the slope at x = 8 is:

m = f'(8) = 15(8)² + 2 = 962.

The line goes through the point (8,f(8)), hence:

f(8) = 5(8)³ + 2(8) + 1 = 2577.

Hence:

y = 962x + b

2577 = 962(8) + b

b = -5119.

Hence the equation is:

y = 962x - 5119.

More can be learned about tangent lines at brainly.com/question/8174665

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