Answer:
The equation of the tangent line to given f(x) in the explicit (slope) form is
y= 7x-2
Step-by-step explanation:
First we must find y coordinate of the point in which tangent touch the function
f(-1)= -3(-1)∧2 +(-1)-5 = -3-1-5= -9 A(-1,-9)=(xa,ya)
We know the equation of the tangent
y - ya = f'(xa) (x - xa)
Now we will find f'(x)
f'(x)= (-3x∧2+x-5)' = (-3x∧2)' + (x)' - (5)' = -6x+1-0 = -6x+1
Now we will find f'(xa) = f' (-1) = -6* (-1) + 1 = 6 + 1 = 7
f'(-1) = 7
now we will replace this value in the equation of the tangent and get
y - (-9) = 7 (x-(-1)) => y+9 = 7(x+1) => y+9 = 7x + 7 => y = 7x+7-9
y = 7x-2
Good luck!!!
