Prove that the curve `y=e^(|x|)` cannot have a unique tangent line at the point `x = 0.` Find the angle between the one-sided tangents to the curve at the point `x = 0.`A. `(pi)/(4) `B. `(pi)/(6) `C. `(pi)/(2) `D. `(pi)/(3) `

Prove that the curve `y=e^(|x|)` cannot have a unique tangent line at

1.	Prove that the curve `y=e^(\|x\|)` cannot have a unique tangent line at the point `x = 0.` Find the angle between the one-sided tangents to the curve at the point `x = 0.`A. `(pi)/(4) `B. `(pi)/(6) `C. `(pi)/(2) `D. `(pi)/(3) `
Answer» Correct Answer - C We have, `y=e^(\|x\|)={(e^(-x)"," , x lt0),(e^(x) "," , x ge 0):} rArr (dy)/(dx)={(-e^(-x)"," , x lt0),(e^(x) "," , x gt 0):} ` The slopes of the tangents at x = 0 to the curves ` y=e^(-x), x lt 0 ` and `y= e^(x), x ge 0 " are " m_(1)=-1 " and " m_(2)=1 ` respectively. Clearly , ` m_(1)m_(2)=-1 ` Hence , the required angle is a right angle.

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Prove that the curve `y=e^(|x|)` cannot have a unique tangent line at the point `x = 0.` Find the angle between the one-sided tangents to the curve at the point `x = 0.`A. `(pi)/(4) `B. `(pi)/(6) `C. `(pi)/(2) `D. `(pi)/(3) `

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