What is the equation of the line tangent to #f(x)=(5+4x)^2 # at #x=7#?
2 Answers
The slope of
Explanation:
The derivative of a function gives the slope of a function at each point along that curve. Thus
This function is
Using the fact that the derivative is linear, so constant multiplication and addition and subtraction is straightforward and then using derivative rule,
This function gives the slope of
y - 264x + 759 = 0
Explanation:
To find the equation of the tangent , y - b = m(x - a ) , require to find m and (a , b ) , a point on the line.
The derivative f'(7) will give the gradient of the tangent (m ) and evaluating f(7) will give (a , b ).
differentiate using the
#color(blue)(" chain rule ") #
# f'(x) = 2(5+4x ) d/dx (5+4x ) = 8(5+ 4x ) # now f'(7) = 8(5+28) = 264and f(7) =
# (5 + 28 )^2 = 1089# now have m= 264 and (a , b ) = ( 7 , 1089 )
equation of tangent : y - 1089 = 264 (x - 7 )
hence y -1089 = 264x - 1848
# rArr y - 264x +759 = 0#