# math

posted by .

Which of the following four fundamental funtions have the same tangent line at x = 0 Ans:_________________ ?

y = x, y = x2, y = x3 and y = ex

• math -

Tangent line at x=0 means to evaluate the derivative at x=0, or f'(0).

For the tangent lines to be equal (coincident), f(0) must also be equal.

y=x => f'(x)=1 => f'(0)=1, f(0)=0
y=x²=> f'(x)=2x => f'(0)=0, f(0)=0
y=x³ => f'(x)=3x² => f'(0)=0, f(0)=0
y=ex =>f'(x)=ex => f'(0)=e0=1, f(0)=1

Therefore there are two sets of tangent lines with equal slopes at x=0, but only one set of them have equal y-intercepts and hence coincident lines.

• math -

For:

y=x

Technically there is no tangent line to a straight line because the definition of tangent means a line a touching at one point.

x^2 and x^3

## Similar Questions

1. ### Calculus - Tangent Line

Hi, im having problems with the following problem. The main issue is actually starting the problem. Find the two points on the curve y = x^4 - 2x^2 - x that have a common tangent line. First, find the derivative of y(x) so that you …
2. ### math

A tangent line is drawn to the hyerbola xy=c at a point P. 1) show that the midpoint of the line segment cut from the tangent line by the coordinate axes is P. 2) show that the triangle formed by the tangent line and the coordinate …
3. ### math repost!!

please help, i procrastinated and now this is due tomorrow!! A tangent line is drawn to the hyerbola xy=c at a point P. 1) show that the midpoint of the line segment cut from the tangent line by the coordinate axes is P. 2) show that …

what are similarities and differences between y=x line and a power funtion with an odd degree?
5. ### cal

find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph …
6. ### Math

Let f(x) be the parabola -x^2+16x-16. find the point (x,y) on f such that tangent line to f at (x,y) passes through the origin. My ans is (8,48). First i do f'x then i find x and lastly i find y. I do this because the max/min point …
7. ### Math

If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent line to the parabola y=3x^2-5x at the point (2,2). My ans is f'(2)=7 & y=7x-12. What is parabola exactly?
8. ### Applied Calculus......

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=6x-5x^2 at (-2, -32) I have to use the four step process, but seem to be getting stuck...
9. ### calculus

Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)
10. ### Calculus

Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = -2x2-2x+1 (-1, -2)

More Similar Questions