The tangent to the curve `y=e^x` drawn at the point `(c,e^c)` intersects the line joining `(c-1,e^(c-1)) and (c+1,e^(c+1))` (a) on the left of `n=c` (b) on the right of `n=c` (c) at no points (d) at all points

Options

A. on the left of x= c
B. on the right of x=c
C. at no point
D. at all points

Answer

1

Explanation

`y=e^(x) rArr (dy)/(dx) = e^(x)`
`therefore "Tangent at" A(c,e^(c )) is `
`y-e^(c ) = e^(c )(x-c)`
`i.e, y = xe^(c )+e^(c )-ce^(c )`
Line PQ is
`y-e^(c-1)=(e^(c+1)-e^(c-1))/((c+1)-(c-1))(x-c-1))`
soliving (i) and (ii)
`x=c+(e^(2)-2e+1)/(-e^(2)+2e+1) lt c`
"therefore Tangent metts the line PQ on the left of" x=c
"A litter: From the graph"