Calculating tangent lines

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Function #f# is given by the function rule #f(x)= 9\cdot \euler^{x}+8\cdot x#. Let #k# be the tangent line to the graph of #f# at #x=1#.

How do we find the formula for #k#? Drag the steps of the solution into the correct order.

#f(1) = 9\cdot \euler+8 #

Enter values of #\rv{x,y}# and #a# in #y=a \cdot x+ b#

#a = f^{\prime}(1) = 9\cdot \euler+8#

#9\cdot \euler+8 = \left ( 9\cdot \euler+8 \right ) \cdot 1 + b#

Calculate the derivative #f^{\prime}(x)#

#b = 0#

Find the #y#-coordinate of the point of tangency

Give the final formula for #k#

Determine the slope #a# of the tangent

Calculate #b#, the #y#-intercept of the tangent

#f^{\prime}(x) = 9\cdot \euler^{x}+8 #

#y = \left ( 9\cdot \euler+8 \right ) \cdot x #

	Description	Calculation
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Differentiation: Applications of derivatives

Calculating tangent lines