Slope & tangent: tangent at x = 2 to f(x) = 3x2 - 2kx + 15 is 3 (& 3 other Qs)

[eriq416]

Slope & tangent: tangent at x = 2 to f(x) = 3x2 - 2kx + 15 is 3 (& 3 other Qs)

Hi! I have 4 questions about finding the slope and equation of a tangent to a curve, thanks so much for helping out

1) Find the value(s) of k so that the slope of the tangent at x = 2 to the curve f(x) = 3x² - 2kx + 15 is 3.

2) Find the equation of the tangent to the curve x³+ 2x² - 5x + 1 when x = 2. Also find where the tangent meets the curve again.

3) Find the equations of the tangents to the curve x⁴ - 2x that pass through the point Q(5,11). (Note that Q does not lie on the curve)

4) The graph y = 5x² + 3x + k has a tangent whose equation is y = 13x + 8. Find the value of k.


If you can solve any of them that would be greatly appreciated!

 

[tkhunny]

Hi! I have 4 questions about finding the slope and equation of a tangent to a curve, thanks so much for helping out

1) Find the value(s) of k so that the slope of the tangent at x = 2 to the curve f(x) = 3x² - 2kx + 15 is 3.

2) Find the equation of the tangent to the curve x³+ 2x² - 5x + 1 when x = 2. Also find where the tangent meets the curve again.

3) Find the equations of the tangents to the curve x⁴ - 2x that pass through the point Q(5,11). (Note that Q does not lie on the curve)

4) The graph y = 5x² + 3x + k has a tangent whose equation is y = 13x + 8. Find the value of k.


If you can solve any of them that would be greatly appreciated!

All can be solved by the application of basic principles.

What is f'(x)? Does it have anything to do with the Tangent Line?

 

[sinx]

Hi! I have 4 questions about finding the slope and equation of a tangent to a curve, thanks so much for helping out

1) Find the value(s) of k so that the slope of the tangent at x = 2 to the curve f(x) = 3x² - 2kx + 15 is 3.

2) Find the equation of the tangent to the curve x³+ 2x² - 5x + 1 when x = 2. Also find where the tangent meets the curve again.

3) Find the equations of the tangents to the curve x⁴ - 2x that pass through the point Q(5,11). (Note that Q does not lie on the curve)

4) The graph y = 5x² + 3x + k has a tangent whose equation is y = 13x + 8. Find the value of k.


If you can solve any of them that would be greatly appreciated!

as tkhunny says;
1) slope=f'(x)=6x-2k
for f'(x)=3, at x=2,
k=?