find the equation of the tangent to the curve `y=-5x^2+6x+7` at the point `(1//2, 35//4)`

Answer

A, D

Explanation

`"For "alpha=1`
`y=|x-1|+|x-2|+x={{:(3-x,, xlt1),(1+x,,1le xlt2),(3x-3,,xge2):}`
`"For "alpha=0, y=3`

`A=(1)/(2)(2+3)xx1+(1)/(2)(2+3)xx1-overset(2)underset(0)int2sqrt(x)dx`
`rArr" "A=5-(8)/(3)sqrt(2)`
`therefore" "F(1)+(8)/(3)sqrt(2)=5`
`"For "alpha=0,y=|-1|+|-2|=3`

`A=6-overset(2)underset(0)int2sqrt(x)dx`
`rArr" "A=6-(8)/(3)sqrt(2)`
`therefore" "F(0)+(8)/(3)sqrt(2)=6`
Note : Solutions of the remaining parts are given in their respective chapters.