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Question
State whether the following statement is True or False:
The equation of tangent to the curve y = 4xex at `(-1, (- 4)/"e")` is ye + 4 = 0
Options
True
False
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Solution
True.
Explanation:
y = 4x ex
∴ `"dy"/"dx" = 4"e"^"x" + 4"xe"^"x"`
Slope of the tangent at `(-1, (- 4)/"e")` is
`("dy"/"dx")_((-1, (- 4)/"e")` `= 4"e"^-1 + 4(-1)"e"^-1`
`= 4/"e" - 4/"e" = 0`
∴ Equation of the tangent at `(-1, (- 4)/"e")` is `("y" + 4/"e")` = 0(x + 1)
∴ ye + 4 = 0
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