Let f(x)=x^2+5. At some point on the graph f(x), the tangent line is parallel to 6x-100. Write down the equation of this line.

Question

aum · Answer

What is the slope of the line 6x - 100 ?

anonymous · Answer

6

aum · Answer

What is the slope of f(x) in terms of x?

anonymous · Answer

are you asking about the slope of f(x)=x^2+5

anonymous · Answer

?

aum · Answer

The first derivative gives the slope of f(x). $$
f(x) = x^2 + 5 \
f'(x) = 2x 
$$

aum · Answer

If two lines are parallel, their slopes must be the same.
Therefore, 2x = 6
x = 3.
when x = 3, f(x) = 3^2 + 5 = 9 + 5 = 14
Therefore, a tangent to f(x) drawn at the point (3, 14) will be parallel to the line 6x - 100.

Equation of the tangent is: y = mx + b
y = 6x + b
(3,14) is a point on the line:
14 = 6*3 + b
b = -4

y = 6x - 4 is the equation of the tangent.

anonymous · Answer

Thank you !!!

aum · Answer

You are welcome.