Let the curve and line intersect at point (x1,y1) ‌y=x2+x+16 ‌‌
dy
dx
|(x1,y1)=2x1+1 Slope of line =‌
y1−0
x1−0
=‌
y1
x1
‌⇒‌‌2x1+1=y1∕x1 ‌⇒‌‌2x12+x1=y1.....(i) (x1;y1) also satisfy the equation of curve. ‌y1=x12+x1+16 ⇒‌‌2x12+x1=x12+x1+16 ⇒x12=16 ‌ or ‌‌x1=4 [only use x1=4 ] If x1=4, then y1=16+4+16=36 m=‌