00:01
Hi, from the question given that y is equal to x squared minus 15 into e to the power of x.
00:13
So here we need to find the point when tangent line is horizontal.
00:33
In general we know that if tangent line is horizontal then slope value is equal to 0, that is d .y by d x is equal to 0.
00:45
So first we need to find derivative of the given expression.
00:48
So d .y by dx is equal to use the product rule.
00:54
So we obtain e to the power of x into 2x plus x squared minus 15 into e to the power of x.
01:05
Now we know that the value of dy by dx is equal to 0.
01:08
So e to the power of x into 2x plus.
01:13
Xxxx minus 15 into e to the power of x is equal to 0 now remove the common term e to the power of x in term x squared plus 2x minus 15 is equal to 0 so now e to the power of x is equal to 0 or xx plus 2x minus 15 is equal to 0 if e to the power of x is equal to 0 as no solution for all x belongs to the real number are.
01:53
Therefore the only possibility is xxx5x plus 2x minus 15 is equal to 0...