Get the solution to "What is the equation of the line tangent..."

Quinn Dean

Answered question

2022-04-08

What is the equation of the line tangent to

f (x) = x^{2} e^{x} - x e^{x^{2}}

at x=0?

unduncjineei5r3

Beginner2022-04-09Added 19 answers

Given,

f (x) = x^{2} e^{x} + x e^{x^{2}}

Differentiate it and find the slope

\frac{d y}{d x} .

Now find the

\frac{d y}{d x} (x = 0)

This slope is the slope of the tangent at that coordinate.
Now find the f(0).

∴ x_{1} = 0, y_{1} = f (0)

∴ x_{1} = 0, y_{1} = 0

Now use the equation of straight lines

\to

y - y_{1} = \frac{d y}{d x} (x - x_{1})

∴ y - 0 = \frac{d y}{d x} (x = 0) \cdot (x - 0)

∴ \frac{y}{x} = \frac{d y}{d x} (x = 0)

Substitute the value of

\frac{d y}{d x} (x = 0)

and get the suitable equation of the tangent.

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