show that the tangent to the curve y=e^x-2x at the point (1,e-2) passes through the origin?

Answer 1

y= e^x - 2x
dy/dx =e^x- 2
at (1,e-2), dy/dx= e^1- 2 = 0.718282
equation of tangent: y- (e^-2) = 0.718282(x-1)
y = 0.718282x -0.718282 + e^-2
y =0.718x -0.5829

since the y-intercept is close to 0,thus this tangent passes thru the origin.

Answer 2

Use each and every little bit of advice which you may desire to get your self a constructive set of linear equations and then resolve. First, all of us be attentive to the parabola passes via (2, 8), so substituting that element into our equation, we get: a(2)^2 + b(2) + c = 8 4a + 2b + c = 8 next, all of us be attentive to that the line y = 2x is tangent to the parabola at x = 0. The slope of this line is two. This tells me that the instant cost of replace at x = 0 is comparable to 2, i.e. the by-fabricated from ax^2 + bx + c at x = 0 is two. d/dx (ax^2 + bx + c) = 2ax + b Now enable x = 0 2a(0) + b = 2 b = 2 We additionally be attentive to that the parabola passes in the time of the element (0, 0) in spite of the undeniable fact that, as a results of fact if the line touches the parabola at x = 0, then they could desire to proportion that element. And substituting x = 0 in the equation for the line yields y = 0. So a(0)^2 + b(0) + c = 0 c = 0 Substituting the numbers for b and c in the 1st equation we've been given: 4a + 2b + c = 8 4a + 2(2) + 0 = 8 4a + 4 = 8 4a = 4 a = a million So the equation of the parabola is y = x^2 + 2x such as you reported.

Answer 3

1. Take the derivative of e^x - 2x.
2. Evaluate it at x = 1
3. Use that value for m in the equation y=mx+b
4. Substitute 1 and e^-2 for x and y in y=mx+b
5. Show that b=0

Easy ☺

Doug

Answer 4

use point-slope to find equation of tangent line
POINT ( 1 , e-2 )

y ' = e^x - 2
y'(1) = e - 2

y - y1 = m(x-x1)
y - (e-2) = (e-2) (x-1)
y-e+2 = (e-2)x - e+2
y = (e-2) x

Plug in x=0 ===> we get y=0!

=]

Answer 5

you need to calculate the derivate at the point (1,e-2), y'=e^x-2 so e^1-2= e-2
so the equation is y=(e-2)x