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11 Let f(r) = I 11 The slope of the tangent line to the graph of f(@) at the point 5, is 5 11 The equation of the tangent line to the graph of f(x) at (-5, is y = ma + b for 5 and b Hint: the slope is given by the derivative at = - 5, ie. f( - 5 + h) -f( -5) lim h-+0 h16 15 14 13 12 4 6 8 10 12 14 16 18 20 22 11 The per capita consumption of breakfast cereal in the US has the following model that appears above c( t ) = -0.0034+ + 0.093t - 0.348t + 12.55 pounds, where t is the number of years since 1990. Decide whether the rate of consumption was changing more rapidly in 2005 or 2012. C' (15) = lbs/year C' (22) = lbs/year The rate was changing more rapidly in @ 2012 2005.Let x] = 3:2 13:: +5 The slope of the tangent line to the graph of ffz} at the point [2, Q] is :l The equation of the tangent line to the graph of ffz} at (2, Q} is y = m: + i? for ME and Hint: the slope is given by the derivative at a: = 2, ie. 2 + h. 2 ( Hm ) }) hH] h Suppose that f is a function given as f} = hf2.": 1. Simplify the expression f[ + h]. fw : + h} - HI} I:. . flit + h} - fie} _ h _ Rationalize the numerator in the difference quotient. [If applies, simplify again.} ff: + h} rim) _ h _ The derivative of the function at I is the limit of the difference quotient as h approaches zero. , . fiz+h}-f{ Weenh _ Simplify the difference quotient, Suppose that the position of a particle is given by 3 = f[t] = HE + t + Q. [a] Find the velocity at time t. wra=Ee {b} Find the velocity at time t = 3 seconds. [:1? {c} Find the acceleration at time t. WES\"3 {d} Find the acceleration at time t = 3 seconds. :1\" 32 O -5 -4/-3 -0 -1 , 123 Select all the points at which the graph above is not differentiable 0-4 0-3 0-2 0-1 01 02 0 3 0 4Suppose that f is a function given as f(x) = - 3x + 1. Simplify the expression f(r + h). f(x + h) = f(x + h) - f(x) Simplify the difference quotient, h f(x + h) - f(x) h The derivative of the function at > is the limit of the difference quotient as h approaches zero. f(x + h) - f(x) f' (x) = lim = h-0 h