Question

find the equation of the tangent to the curve y = 9x² - 12x + 7 which is parallel to the x-axis​

Answer 1

$\sf\huge {\underline{\underline{{Solution}}}}$

Since,the line is parallel to the x-axis.So, therefore it's slope (m) will be zero.

We have to solve and find its derivative first and then set it equals to zero where the slope is zero.

=> let the f(x) = 9x²-12x+7

=>f'(x)= 9*2x-12(1)

=>f'(x)= 18x-12

=> f'(x) =0

=> 18x-12=0

=> 6(3x-2)=0

=>3x-2=0

=>3x=2

x= 2/3

Equation of line when tangent is given:

$\sf \: \boxed{m = \frac{y - yo}{x - xo} }$

Since m(slope) is zero so,our equation becomes

=> y-yo= m(x-xo)

=>y-yo= 0(x-xo)

=>y-yo=0

y=yo

Equation of the tangent = y-yo

Answer 2

Answer:

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